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Re: Re: Re: Re: RE: Re: Sometimes <space> means multiple

  • To: mathgroup at
  • Subject: [mg75474] Re: [mg75442] Re: [mg75426] Re: [mg75423] Re: [mg75364] RE: [mg75358] Re: Sometimes <space> means multiple
  • From: Andrzej Kozlowski <akoz at>
  • Date: Wed, 2 May 2007 03:51:46 -0400 (EDT)
  • References: <> <> <> <>

I think I can see some advantages to "intellectual laziness". It 
might, for example, stop people writing long posts when they have no 
point to make.

So to make it short: it was already pointed by someone else that 
Mathematica's use of "space" for multiplication is simply the nearest =

approximation to using nothing at all - by far the most common 
convention in algebra. Mathematica does allow "nothing" to be used 
when  no ambiguity results; in other cases space is used, which 
approximates rather well what one can see in books an d papers on 
In InputForm asterisk is used because central dot is not available in =

ASCII and ordinary dot is used, naturally, for dot product. Asterisk 
is sometimes used in books on algebra do denote binary operations, 
probably more often than "x" (which can, of course,  be used in 
TraditionalForm in Mathematica).
Intellectual laziness (presumably due to infection) prevents me from 
writing any more on this subject.

Andrzej Kozlowski

On 1 May 2007, at 16:19, J=E1nos wrote:

> I think the reason for "space" used as multiply is the typical anglo-
> american intellectual laziness :)  /Old Hungarian proverb:  "Whose
> shirt it is not, should not take it on"/
> Steve just did not want to type an extra character when he came up
> with the design - that is it.  He was also constrained by the ASCII =

> 7 =
> bit.
> If I look back on my education for multiplication in elementary
> school a dot was use on the "middle of the lane".  On a Mac it is
> <Option>+<Shift>+<9>.
> Now to use that would have been more painful than just <Shift>+<8>,
> wouldn't it ?.
> The <Shift>+<8> came to the math circles via computers and with 
> punch =
> cards where the restrictive ASCII 7 bit ruled the world and "a" and
> "b" had to be tightened with SOMETHING.
> Looking many professional journal pdfs one thing is sure.  Neither
> the "space" nor the "star" is used for multiplication.  It is still
> the dot on the "middle of the lane", a small "x" or nothing.  That
> is, I never see "a*b" or "a b" as a multiplication of a and b but
> rather I see "ab" or "a=B7b".
> With the best,
> J=E1nos
> P.S.  If I take the "a b" to its ultimate test and "try" it in pre-
> fix " ab" or post-fix "ab " that shows clearly the dumbness of the
> usage of space in its pure naked form :)
> On Apr 30, 2007, at 3:38 AM, Andrzej Kozlowski wrote:
>> I compltely agree. I also think that any comparisons between C++ and
>> Mathematica in this respect are completely off the mark, unless of
>> course sombody decides to develop an analogue of "TradtitionalForm"
>> for C++.
>> I would also like to point out the following obvious but not
>> insignificant fact. Enter  a b (or 2 3  if you prefer) and convert to
>> InputForm. You will obtain an explicit asterisk in place of the
>> space. Conversely, enter a*b and convert to TraditionalForm (or even
>> StandardForm). You will get a space instead of the asterisk. This, in
>> my opinion,  is exactly how it should be. In fact, I am somewhat
>> shocked that anyone would claim otherwise.
>> Andrzej Kozlowski
>> On 29 Apr 2007, at 16:14, Murray Eisenberg wrote:
>>> Why "mistake"?  Why not allow Mathematica to mimic as much of
>>> traditional mathematical notation as possible without running into
>>> genuine ambiguity?
>>> After all, it's really convenient to be able to use 2 Exp[x] and
>>> Cos[2
>>> t] -- and even 2Exp[x] and Cos[2t] -- without having to insert an
>>> extra,
>>> distracting multiplication symbol.  Then the usage in 2 4, for
>>> example,
>>> just extends that.
>>> In my own work, I ordinarily include an explicit multiplication
>>> symbol
>>> -- and I prefer the multiplication sign one gets from Esc * Esc
>>> instead
>>> of the FORTRANish * -- when the factors are numbers.  There's
>>> nothing to
>>> prevent you from doing that if you don't like the implicit
>>> multiplication indicated by a space.
>>> Virgilio, Vincent - SSD wrote:
>>>> Personally, I think it was a mistake to overload the meaning of
>>>> "space"
>>>> to multiply. I bet Wolfram Inc. would reverse that decision now,
>>>> if it
>>>> wasn't for backward compatibility.
>>>> I like to compare Mathematica to C++. Somewhere in his writings,
>>>> Bjarne
>>>> Stroustrup mentions the same issue, and his decision not to 
>>>> overload
>>>> whitespace. I think the question also arises on the Boost mailing
>>>> lists
>>>> now and then, mostly tongue-in-cheek.
>>>> (Corrections welcome.)
>>>> Vince Virgilio
>>>> -----Original Message-----
>>>> From: Bill Rowe [mailto:readnewsciv at]
>>>> Sent: Thursday, April 26, 2007 3:35 AM
>>>> To: mathgroup at
>>>> Subject: [mg75364] [mg75358] Re: Sometimes <space> means
>>>> multiple , sometimes not
>>>> On 4/25/07 at 5:27 AM, siewsk at wrote:
>>>>> As a newbie, I was taught that <space> character in Mathematica
>>>>> means
>>>>> multiple. But sometimes it does not.
>>>>> For example:
>>>> <examples snipped>
>>>> Mathematica allows spaces to be placed before or after any
>>>> operation.
>>>> Consequently, a space is only interpreted as a multiply when there
>>>> is no
>>>> other operator or other possible interpretation.
>>>> So, -4 -2 is the same as -4 - 2 or -4-2 and gives -6 but
>>>>      -4 (-2) will yield 8
>>>> --
>>>> To reply via email subtract one hundred and four
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>>> --
>>> Murray Eisenberg                     murray at
>>> Mathematics & Statistics Dept.
>>> Lederle Graduate Research Tower      phone 413 549-1020 (H)
>>> University of Massachusetts                413 545-2859 (W)
>>> 710 North Pleasant Street            fax   413 545-1801
>>> Amherst, MA 01003-9305
> ----------------------------------------------
> Trying to argue with a politician is like lifting up the head of a
> corpse.
> (S. Lem: His Master Voice)

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